SOLUTION: Express (3+2i)(6-i)/(2+i)(4+2i) in a + bi form. Round a and b to hundredths.
Thanks for any help!
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Question 252055: Express (3+2i)(6-i)/(2+i)(4+2i) in a + bi form. Round a and b to hundredths.
Thanks for any help!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
FOIL the numerator and denominator remembering that 
(6\,-\,i)}{(2\,+\,i)(4\,+\,2i)}\ =\ \frac{20\,+\,9i}{6\,+\,8i})
Form the conjugate of the denominator, that is change the sign in the middle, 
.
Multiply your fraction by 1 in the form of the conjugate of the denominator divided by itself. Note the difference of two squares result in the denominator:
\left(\frac{6\,-\,8i}{6\,-\,8i}\right)\ =\ \frac{192\,-\,106i}{36\,-\,(-64)}\ =\ \frac{192\,-\,106i}{100}\ =\ 1.92\,-\,1.06i)
John
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